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Topic: Cork, Burlap Bag, and Irregular Bottle (Read 8742 times) |
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towr
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #25 on: Jan 12th, 2004, 12:33pm » |
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TenaliRaman, I don't really see what your reply adds to CMR post, since he says the same thing in his second paragraph..
In any case SWF allready suggested the same thing earlier..
And with very irregular shapes it simply won't work.. The water has to be able to flow freely. If for instance you have something like an upside down glass trapped inside the bottle then when you turn it upside down, there won't necessarily be just one water level, but one for the glass and one for the rest of the bottle.
And you can easily further complicate the shape of the bottle..
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SWF
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #26 on: Jan 12th, 2004, 5:10pm » |
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Thank you for noticing, towr. Also, the following comment about the centroid is false:
on Jan 12th, 2004, 11:16am, CMR wrote:| ...the water line will be at the same place on the bottle if you flip the bottle exactly 180 degrees. It will be at the level of the geometric centroid. |
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Even for a simple shape like a cone with its axis oriented vertically, if half filled, the water line does not pass through the centroid.
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #27 on: Jan 14th, 2004, 11:02am » |
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Hey, the answer has been found!
lol
What you do is:
Rip a string from the burlap. Take a bit of tyh water in your mouth and cork the bottle. Look at the water line, tie the string so it wraps around at that point, and then flip the bottle. Use that to estimate if there is too much or too little water in it (if at middle, water level will be the same as before flipped). If too much, sip a bit more; if too little, spit some back.
Nice job workin on the problem.
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william wu
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #28 on: Jan 14th, 2004, 7:18pm » |
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on Jan 14th, 2004, 11:02am, Sklarface wrote:Hey, the answer has been found!
lol
What you do is:
Rip a string from the burlap. Take a bit of the water in your mouth and cork the bottle. Look at the water line, tie the string so it wraps around at that point, and then flip the bottle. Use that to estimate if there is too much or too little water in it (if at middle, water level will be the same as before flipped). If too much, sip a bit more; if too little, spit some back.
Nice job workin on the problem. |
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Part of me thinks it's kind of clever, but another part of me says  Some aspects of the solution I dislike include 1) Inaccuracies induced by saliva backwash, and importantly, 2) you need a level surface to rest the bottle on such that the water level can be properly "roped" by the burlap string. However, no such surface or table is stipulated in the problem. If the floor is flat, that would work; but for all we know you could be standing on a grassy hill.
Furthermore, even if assume we have such a surface, and we ignore bottles for which the water level is not the same when the bottle is half full inverted, we still need the bottle's centroid to be such that the bottle doesn't tip over when stood on either its bottom or its corked top. Maybe you could get away with using your hands to hold the unstable bottle against the level surface, but that leaves you with the problem of simultaneously roping the thread to mark the water level AND keeping the bottle from tipping over. Quite difficult -- you'd probably have to get your feet involved, or other parts of the body in some contorted position.
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| « Last Edit: Jan 15th, 2004, 5:40am by william wu » |
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle  half.bmp
« Reply #29 on: Jan 15th, 2004, 2:21pm » |
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Well, william, thats true, it would be hard if it doesnt have a flat surface. And saliva would play a part (though you could just sit there till you almost died from dehydration...). The part about "and we ignore bottles for which the water level is not the same when the bottle is half full inverted," wouldnt matter, I thought it would, but.. it doesnt. lol. If you have half the bottle full, and you tip it over, the water level will remain the same. Ill draw a drawing, lol. See attatched.
Anyway, thanks everyone for working on the problem. Interesting one (is it bein added to any of the riddle pages?).
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Sklarface
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #31 on: Jan 15th, 2004, 5:18pm » |
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lol, it wouldnt matter how F^d up the bottle is, to the line will be the bottom 50% of the volume, flip it, still 50% of the bottle.
Doesnt make sense, but...
Try it! I tried it (lol, quite a sight to see, had water everywhere), but it does work. And, if you think you have some irregularly shaped bottles, wait till you come over here to WV... lol
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towr
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #32 on: Jan 16th, 2004, 12:47am » |
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When my bottle is filled, and you turn it upside down to let some water out, there won't be one water surface left, but multiple.
Moreso, when you turn it back right side up, there will again not be just one water-surface, and different ones than the time before..
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| « Last Edit: Jan 16th, 2004, 12:48am by towr » |
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towr
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I could probably design bottle that are a lot more evil than this.. But I hope this attachment will show why this one is bad enough as it is..
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Margit
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #34 on: Jan 16th, 2004, 1:44am » |
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Well, I must say that if this is indeed the "solution", then I am very disappointed not to say disgusted.
My comments :
You must have very different burlap bags over your side of the pond. I cannot get any sort of regular piece of material from the bag, let alone a string. Using both hands and feet, I can succeed in tearing it into useless irregular pieces.
I said we needed constraints on the bottle. You need to be able to see into it. I have many bottles where this is not the case including whiskey, cognac, wine bottles not to mention kitchen items such as oil and vinegar bottles.
I'd like to see somebody try it with one of these :
http://www.kleinbottle.com/
And, of course, the larger the bottle, the greater the error margin. The problem states "exactly half". Try it with a
Nebucandnezzar champagne bottle.
Just not very satisfying at all.
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towr
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #35 on: Jan 16th, 2004, 2:27am » |
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on Jan 16th, 2004, 1:44am, Margit wrote:If we go by their claim, than a klein bottle has no volume, so a full one is an empty one is a half full one, so you're done before you start..
(Of course despite their zero-volume claim it can conatin something, which means it doesn't have zero volume)
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CMR
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #36 on: Jan 16th, 2004, 11:55am » |
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on Jan 12th, 2004, 5:10pm, SWF wrote:Thank you for noticing, towr. Also, the following comment about the centroid is false:
Even for a simple shape like a cone with its axis oriented vertically, if half filled, the water line does not pass through the centroid. |
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SWF:
Maybe I am wrong, but if the water line does not pass through the centroid, where does it pass through? I thought the definition of the geometric centroid was the centre of mass (or volume) of a 3 dimensional object.
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John_Gaughan
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #37 on: Jan 16th, 2004, 4:21pm » |
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If you have an irregular bottle like in towr's diagram, you do not have a single water line. Sure, maybe one does pass through the centroid, but which one? If so, it would be a coincidence, and it would not necessarily mean you have half of the bottle left.
I still think the idea of a burlap bag absorbing water is ludicrous. One of the characteristics of burlap material is that it is extremely pourous and while the individual strands may not be water-repellant, they aren't exactly sponges, either.
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SWF
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #38 on: Jan 16th, 2004, 6:24pm » |
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on Jan 16th, 2004, 11:55am, CMR wrote:
Maybe I am wrong, but if the water line does not pass through the centroid, where does it pass through? I thought the definition of the geometric centroid was the centre of mass (or volume) of a 3 dimensional object. |
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For a general shape, there is not a point that a plane dividing the volume in half always passes through. It will pass through the centroid in certain circumstances such as when it is a plane of symmetry.
Centroid is a 'balance' point, but that does not mean half of the volume is on each side of it. Whether something balances also depends on how far things are from the balance point. For example, an adult on a seesaw can balance with a small child if the adult sits close to the pivot point. When they balance, the pivot point is below the centroid, but more than half the weight is on the adult's side.
CMR, the way you quoted me makes it look like I am claiming my own statement is false.  I know it is unintentional- the board leaves out previous quotes inside of quotes.
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Margit
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #39 on: Jan 17th, 2004, 4:04am » |
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Well, I would suggest that we lock Sklarface's teacher and the chem teacher into a room where there is :
a) An unlimited supply of water
b) An opaque regular bottle
c) A Klein bottle (either opaque or not)
d) Corks to fit the afore mentioned bottles
e) Two burlap bags (USA/Europe)
and let them out when they think they can produce a corked bottle that is "exactly half full".
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Icarus
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #40 on: Jan 18th, 2004, 12:12pm » |
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That would be interesting for the Klein bottle alone. A true klein bottle does not exist in 3-dimensional space, so what we are left with showing is nothing but a self-intersecting fraud.
If we lock them in with a real Klein bottle, can I go along? I'd love to see one! (And yes, a real Klein bottle has 0 volume because it isn't really a bottle: it has no interior.)
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rmsgrey
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #41 on: Jan 20th, 2004, 9:33am » |
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If you want to be picky, an opened ordinary bottle has no well defined volume - the boundary between "interior" and "exterior" is a matter of opinion. If you define volume along some scheme such as the maximum volume of fluid that can be carried by the bottle under standard conditions, then a Klein bottle has a non-zero volume.
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Icarus
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #42 on: Jan 20th, 2004, 4:45pm » |
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Nay - that is once again the case for our pseudoklein bottle only. A real klein bottle, such as exists only in 4 or more dimensional space, is incapable of enclosing a volume. Indeed the very concept of it's volume is hard to define. As an example, consider a circle in the plane. Its area is easily defined, and since the formula is well-known, easily calculated. Now bend half of the circle up at a right angle to the plane. What is the area of the bent circle? The concept lacks a good definition.
The same thing is true of the klein bottle, which requires such a bend out of 3D to even exist.
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rmsgrey
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Re: Cork, Burlap Bag, and Irregular Bottle
« Reply #43 on: Jan 22nd, 2004, 8:10am » |
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But you can surely still hold 2D "water" in such a folded circle, or in a Mobius Strip. Any situation in which a Klein Bottle can exist runs into the problem of what prevents the water from leaking out of the "sides" of the ordinary bottle anyway, so I suspect that any attempt to define capacity in such a way that an ordinary 3D bottle has a non-zero capacity while a Klein Bottle doesn't, while still being applicable to the riddle, will either fail, or simply not apply to the klein bottle, in which case, I suspect, a reasonable extension will. Of course, this is such a sweeping statement, I'm at least half expecting it to be disproved, but lacking a Klein Bottle (and, for that matter not having a tap handy at the moment) I'm not in a position to determine experimentally whether or not it wil hold water.
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